I have to admit that on this one machine I did bungle the upgrade from LMDE to LMDE2: Stupid me forgot Step 1, pointing the the APT sources to Jessie before doing the rest up to dist-upgrade… When I finally noticed this, I repeated the process correctly and it seems to be quite fine now — except an authentication problem: mintupdate, auto-mounting of USB-drives and shutting down do not work anymore, I have to sudo these.

Yay! All is well again, thank you Zill!
pam-auth-update made its own backup copies *.pam-old so the first step wasn't needed at all.
Just for information, the changed files/lines in /etc/pam.d were —
• in common-auth removal of auth optional pam_cap.so
• in common-password from pam_mate_keyring.so to pam_gnome_keyring.so
• in common-session added session optional pam_systemd.so